# 15+Root+Locus+Design+Concepts++w+alt+text ```Root Locus Design
Concepts
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Control System Including a Delay
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First-Order Time Lag Plus Dead Time
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Root Locus without Delay (T = 0;
Gp(S) = 1/S); H(S) = 1
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Root Locus with Delay (T = 1; K varies)
• &gt;&gt; n=[-1 2] ;d=[1 2 0];
• &gt;&gt; r=rlocus(n,d);
• &gt;&gt; plot(r,'-');
• &gt;&gt;v=[-3 10 -3 3]; &gt;&gt;axis(v);
• &gt;&gt;axis('square')
• &gt;&gt; grid
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Root Locus with Delay (K = 2; 1/T varies)
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Conclusion
• As a system is driven at larger gains (faster response), the value of the
delay must be smaller for stability.
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System to be Compensated
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Proportional Compensated R-L
[Gc(S)Gp(S) = K/(S + 2)2
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Step Response for T(S) = K/(S2 + 2S + K + 1) and K = 1
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Integral-Compensated Root Locus
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Step Response with K = 1
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Proportional–Plus-Derivative compensated R-L
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Step Response for T(S) = K(S + 2)/[S2 + (2 + K)S + 2K]
and K = 1
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Light-Source Tracking System
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Block Diagram
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Root Locus
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Typical Responses to Step
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Block Diagram with Position and Rate
Feedback
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Signal Flow Graph
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Unit Step Response with K = 250;
K’ = 0.08
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```